Today's state is separate from the Church, isn't it?

I have just remembered an interview with Germany's contemporary Chancellor Angela Merkel, as in this interview, one member of the audience asked her, in a rather pathetic tone, suggesting she had to reply yes if she wanted to qualify as Germany's Chancellor, whether she believed in "God". He was, needless to say, referring to the monotheistic god of the Abrahamitic religions (therefore I capitalized the word), more specifically, in turn, to the Christian god. Mrs. Merkel, however, shied away from directly answering the question. Her response, nevertheless, betrayed her lack of belief in the monotheistic god more clearly than she might have expected: "Och, ich finde den Gedanken, dass da einer is', der auf uns alle aufpasst, eigentlich ganz schön,"* replied she (although her exact words may have been slightly different).
She neither said openly that she did not believe in God nor the opposite and thus handled the question really skilfully.

Now, in Germany the state and the Church are formally separated. Notwithstanding, all priests get their income from the state instead of the Church's own funds, each religious institution gets financial support from public funds, and none of the actual members of the Bundestag dare say a word against religion or the churches. Even though it is quite obvious that there are more politicians in Germany who do not believe in any deity whatsoever, they simply do not dare come out. Some parties, such as the CDU (Christlich Demokratische Union) and its sister party, the CSU (Christlich Soziale Union), still bear the word 'Christian' in their names, yet should they not give more value to the second part of their respective names? 'Democratic' and 'social', that is what they should stand for, albeit they originated in a Christian cotext.
And although I am clearly drawn to the political left, in my view, each politician should be allowed to speak out their real beliefs, no matter to which party they belong. Thus, if a politician is a nonbeliever, he must be allowed to say so in order to be able to answer a question like the one Mrs. Merkel was asked in the aforementioned interview honestly.

In general, many people tend to blame politicians for everything wrong, even though it is we, the people, who define the bounds of their actions. If we do not even allow them to speak their mind, we must not expect them to be honest to us with respect to other concerns. If politicians behave in an unacceptable manner, it is a challenge to us, the people, to do something about it. If we choose to be silent, it is no wonder that they will go on violating even more rights, laws, and orders.

Now, I would like to know how the situation is like in other countries and continents. How much separation between state and Church--or churches--is there really, if at all? What are our real and legal possibilities to do something about it?

Naturalistic regards,

Markus

*"O well, I find the belief that there is some guy ("einer") looking after all of us quite soothing ("ganz schön")." (Translation by me)